Tangential Acceleration Problem.

In summary, the conversation involved a person asking for help in finding the tangential acceleration for three cars traveling at 21 m/s along a hilly road. They mentioned trying to use the formula for radial acceleration, but were unsure of how to calculate alpha without any given times. They also mentioned needing a relation between radial and tangential accelerations.
  • #1
Shipman515
7
0
Okay. So I've got three cars that are traveling along a hilly road. One is at the beginning, where its flat, one is at the bottom of the hill, one is at the top. Each is traveling at 21 m/s. I am supposed to find tangential acceleration for each.

I tried:
a = v^2 / r but that is radial acceleration.
I know the formula for tangential acceleration is a = (alpha)(r)

but i am given no times or anything to calculate alpha.


I'm thinking I need a relation of some sort between radial and tangential accelerations.

Anyone have any guidelines?
 

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  • #2
Guess I should have posted this in homework help section. Apologies, I will from this point on.
 
  • #3


I would first clarify the problem by asking for more information such as the radius of the hill and the time it takes for each car to reach the top or bottom of the hill. Without this information, it is difficult to calculate the tangential acceleration for each car.

Assuming that the cars are all traveling at a constant speed of 21 m/s and the hill is a perfect circle with a radius of 100 meters, we can use the formula a = v^2 / r to calculate the radial acceleration for each car. The car at the bottom of the hill would have a radial acceleration of 0 m/s^2 since it is traveling along a straight path. The car at the top of the hill would have a radial acceleration of -0.44 m/s^2 (negative because it is moving in the opposite direction of the car at the bottom). The car at the beginning of the flat road would also have a radial acceleration of 0 m/s^2.

To find the tangential acceleration for each car, we can use the formula a = alpha * r. Since we know the radial acceleration for each car, we can rearrange the formula to solve for alpha. So for the car at the bottom of the hill, alpha would be 0 m/s^2 / 100 m = 0. The car at the top of the hill would have an alpha of -0.44 m/s^2 / 100 m = -0.0044 m/s^2. And the car at the beginning of the flat road would also have an alpha of 0 m/s^2 / 100 m = 0.

In conclusion, without more information, it is difficult to accurately calculate the tangential acceleration for each car. However, we can use the given information to calculate the radial acceleration for each car and use that to find the alpha, or tangential acceleration, for each car.
 

What is tangential acceleration?

Tangential acceleration is a measure of how the speed of an object changes over time as it moves along a curved path.

How is tangential acceleration different from linear acceleration?

Tangential acceleration describes the change in speed of an object moving along a curved path, while linear acceleration describes the change in speed of an object moving in a straight line.

What factors affect tangential acceleration?

Tangential acceleration is affected by the object's speed, the radius of the curved path, and the object's mass. It also depends on the forces acting on the object, such as centripetal force.

How is tangential acceleration calculated?

Tangential acceleration can be calculated using the formula aT = v^2/r, where aT is tangential acceleration, v is the object's speed, and r is the radius of the curved path.

Why is tangential acceleration important in science?

Tangential acceleration is important because it helps us understand the motion of objects moving along curved paths, such as satellites orbiting the Earth or cars going around a curve. It also plays a role in various engineering and physics applications, such as roller coasters and centrifuges.

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